Concerning the two horseshoe objects above in the reply nr 36 : they interchange orbits and seem to be in close counterphase to each other . ( when one is in the outer orbit the other is in the inner ) The last statement is not true as can be seen from the plot hereunder , where the distance to the sun and the velocities are represented . Both bodies have a cycle of about 115 years , but there seems to be a phase lag of about 15 years between the time the bodies change the orbit . This means there are times where they are at the some distance to the sun ( but at this moments they are about 360-~60 =~300 degrees separated ) .

The orbital exchange happens when they are near each other, and can alter each other's orbits. áThis graph is similar to the graph of Janus and Epimetheus, except Janus and Epimetheus do not have similar masses:

Is there a third body involved in the case of Janus and Epimetheus ? In the case of the two asteroids in the Lagrangian orbit I have the impression that the change takes place when one body is near to one Lagrangian body (look at the rotating frame in the beginning ) ; if the 2nd ast approaches the other Lagrangian body this asteroid also changes orbit .

I've been playing aroud with a twin Earth-Moon system , placed right opposite to our sun , so at 180░ . Adding a small exces velocity of 1m/s makes the system move after about 100 years . The result may be seen here in a rotating frame aroud Earth. The second moon was made invisible . The system gets in a horseshoe orbit to Earth . It has tendency to approach Earth from left to right alternatively .